Problem: Simplify the following expression: $ t = \dfrac{7}{10} + \dfrac{-r + 3}{10r} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10r}{10r}$ $ \dfrac{7}{10} \times \dfrac{10r}{10r} = \dfrac{70r}{100r} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-r + 3}{10r} \times \dfrac{10}{10} = \dfrac{-10r + 30}{100r} $ Therefore $ t = \dfrac{70r}{100r} + \dfrac{-10r + 30}{100r} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{70r - 10r + 30}{100r} $ $t = \dfrac{60r + 30}{100r}$ Simplify the expression by dividing the numerator and denominator by 10: $t = \dfrac{6r + 3}{10r}$